Answer
$\dfrac{\sqrt{5}+2}{\sqrt{2}}=\dfrac{1}{\sqrt{10}-2\sqrt{2}}$
Work Step by Step
$\dfrac{\sqrt{5}+2}{\sqrt{2}}$
Multiply the numerator and the denominator by the conjugate of the numerator and simplify if possible:
$\dfrac{\sqrt{5}+2}{\sqrt{2}}=\dfrac{\sqrt{5}+2}{\sqrt{2}}\cdot\dfrac{\sqrt{5}-2}{\sqrt{5}-2}=\dfrac{(\sqrt{5})^{2}-2^{2}}{\sqrt{2}(\sqrt{5}-2)}=...$
$...=\dfrac{5-4}{\sqrt{10}-2\sqrt{2}}=\dfrac{1}{\sqrt{10}-2\sqrt{2}}$
